Running Boundary Condition

In this paper we argue that boundary condition may run with energy scale. As an illustrative example, we consider one-dimensional quantum mechanics for a spinless particle that freely propagates in the bulk yet interacts only at the origin. In this setting we find the renormalization group flow of U(2) family of boundary conditions exactly. We show that the well-known scale-independent subfamily of boundary conditions are realized as fixed points. We also discuss the duality between two distinct boundary conditions from the renormalization group point of view. Generalizations to conformal mechanics and quantum graph are also discussed.Comment: PTPTeX, 21 pages, 8 eps figures; typos corrected, references and an appendix adde

Career readiness for all

The goal of the Coalition for Career Development is to make career readiness the first priority of American education. Our vision is to ensure that ALL students secure productive employment in their chosen pathway as efficiently and cost-effectively as possible.Accepted manuscrip

Relaxed sector condition

In this note we present a new sufficient condition which guarantees martingale approximation and central limit theorem a la Kipnis-Varadhan to hold for additive functionals of Markov processes. This condition which we call the relaxed sector condition (RSC) generalizes the strong sector condition (SSC) and the graded sector condition (GSC) in the case when the self-adjoint part of the infinitesimal generator acts diagonally in the grading. The main advantage being that the proof of the GSC in this case is more transparent and less computational than in the original versions. We also hope that the RSC may have direct applications where the earlier sector conditions don't apply. So far we don't have convincing examples in this direction.Comment: 11 page

Enhancement of reliability in condition monitoring techniques in wind turbines

The majority of electrical failures in wind turbines occur in the semiconductor components (IGBTs) of converters. To increase reliability and decrease the maintenance costs associated with this component, several health-monitoring methods have been proposed in the literature. Many laboratory-based tests have been conducted to detect the failure mechanisms of the IGBT in their early stages through monitoring the variations of thermo-sensitive electrical parameters. The methods are generally proposed and validated with a single-phase converter with an air-cored inductive or resistive load. However, limited work has been carried out considering limitations associated with measurement and processing of these parameters in a three-phase converter. Furthermore, looking at just variations of the module junction temperature will most likely lead to unreliable health monitoring as different failure mechanisms have their own individual effects on temperature variations of some, or all, of the electrical parameters. A reliable health monitoring system is necessary to determine whether the temperature variations are due to the presence of a premature failure or from normal converter operation. To address this issue, a temperature measurement approach should be independent from the failure mechanisms. In this paper, temperature is estimated by monitoring an electrical parameter particularly affected by different failure types. Early bond wire lift-off is detected by another electrical parameter that is sensitive to the progress of the failure. Considering two separate electrical parameters, one for estimation of temperature (switching off time) and another to detect the premature bond wire lift-off (collector emitter on-state voltage) enhance the reliability of an IGBT could increase the accuracy of the temperature estimation as well as premature failure detection

Optimizing condition numbers

In this paper we study the problem of minimizing condition numbers over a compact convex subset of the cone of symmetric positive semidefinite $n\times n$ matrices. We show that the condition number is a Clarke regular strongly pseudoconvex function. We prove that a global solution of the problem can be approximated by an exact or an inexact solution of a nonsmooth convex program. This asymptotic analysis provides a valuable tool for designing an implementable algorithm for solving the problem of minimizing condition numbers

Normality condition in elasticity

Strong local minimizers with surfaces of gradient discontinuity appear in variational problems when the energy density function is not rank-one convex. In this paper we show that stability of such surfaces is related to stability outside the surface via a single jump relation that can be regarded as interchange stability condition. Although this relation appears in the setting of equilibrium elasticity theory, it is remarkably similar to the well known normality condition which plays a central role in the classical plasticity theory